Tools & Resources
Curated extras for Topic 5: interactive tools, supplemental videos, and references. Pick what helps. Skip what doesn't.
Hands-on widgets for poking at the math. Drag a slider, watch the line move.
Normal Distribution Explorer
Drag the mean, the standard deviation, and a cutoff value. The bell curve shifts and resizes; the empirical-rule bands recolor; the shaded P(X < x) region updates in real time. Watch what "two standard deviations from the mean" actually means.
Center & Spread Visualizer
Paste a list of numbers, get the mean / median / mode / range / sample SD, and see them plotted on a dot plot. Flip on the outlier toggle to watch the mean lurch while the median holds — the central insight of why we use the median for skewed data.
Mean, Median, and Mode — Crash Course Statistics #3
Defines all three measures of center and shows how outliers skew the mean (Middle Ages life-expectancy example, then income skew). The central insight of this section in one video.
Mean, Median, Mode, and Range — How To Find It!
Procedural companion to the Crash Course conceptual video. Methodical worked examples for odd and even data sets — the plug-and-chug skill students need.
How To Calculate The Standard Deviation
Walks through s = √(Σ(x − x̄)² / (n − 1)) step by step with two examples, explicitly explaining why we divide by n − 1. Exactly the formula in this lesson.
Measures of Spread — Crash Course Statistics #4
Conceptual framing of range, variance, and SD as 'typical distance from the mean.' Pairs well with OCT's procedural treatment above.
Charts Are Like Pasta — Crash Course Statistics #5
Bar charts, pie charts, pictographs, and histograms with the categorical-vs-quantitative distinction — the basis of the 'bars touching vs bars with gaps' rule. Strongest single-video coverage of multiple display types.
Plots, Outliers, and Justin Timberlake — Crash Course Statistics #6
Companion episode covering box plots, line charts, and scatter plots — fills the gaps left by #5 in the data-display landscape.
ck12.org Normal Distribution Problems: Empirical Rule
Sal works the 68-95-99.7 rule explicitly with a numeric example, including a 'what percent above the mean + 2σ' style computation — exactly the application this lesson asks for.
The Normal Distribution, Clearly Explained!!!
Short, intuitive intro to the bell curve and the '≈95% within 2σ' rule using baby vs adult heights. Pair with Khan's worked example above — concept first, then computation.
Sampling Methods and Bias with Surveys — Crash Course Statistics #10
How polls actually work: sample, population, sources of bias. Doesn't compute margin of error itself — pair with the confidence-intervals video below.
Confidence Intervals — Crash Course Statistics #20
The '47% support, ±3%' polling framing is directly demonstrated using the election-polling example. Note: this episode crosses slightly into z-score territory after ~7 minutes — for a 100-level audience, watch the first portion (polling + margin of error) and stop before the z-score formulas.